If a child flips a coin five times in a row, what is the probability that she will receive at least one head and one

[BTGmoderatorDC]

If a child flips a coin five times in a row, what is the probability that she will receive at least one head and one tail?

A) 3/4
B) 11/12
C) 15/16
D) 31/32
E) 63/64


OA C

Source: Veritas Prep

[Brent@GMATPrepNow]

If a child flips a coin five times in a row, what is the probability that she will receive at least one head and one tail?

A) 3/4
B) 11/12
C) 15/16
D) 31/32
E) 63/64


OA C

Source: Veritas Prep

If a coin is flipped 5 times in a row, there are 32 possible outcomes (HHTTH, HTHTT, TTTTT, etc)
How did we get 32?
Well, there are 2 possible outcomes for the 1st coin flip, 2 possible outcomes for the 2nd coin flip, 2 outcomes for the 3rd flip, 2 outcomes for the 4th flip, and 2 outcomes for the 5th flip,
By the Fundamental Counting Principle (FCP), the TOTAL number of outcomes when flipping 5 coins = (2)(2)(2)(2)(2) = 32

Of course, among those 32 outcomes, there are some outcomes that DO NOT meeting the required condition that we receive at least one head and one tail
There are EXACTLY 2 outcomes that DO NOT meet this required condition.
They are: TTTTT and HHHHH

So, the number of outcomes that DO meet the required condition = 32 - 2 = 30

So, P(child gets at least one head and one tail) = 30/32= 15/16

Answer: C

Cheers,
Brent

[regor60]

Not satisfying the condition would mean either all heads or all tails.

Probability of either is 1/2^5 = 1/32.

Since there are two, 2*1/32= 1/16.

All other outcomes satisfy, so

1-1/16= [spoiler]C, 15/16[/spoiler]